CS International
CSE Physics (Chapter 5 Momentum)
Two equally weighted objects of mass m are moving in opposite directions, one with half
the velocity of the other. If they collide and stick together, what is the resultant
velocity in terms of the faster object’s velocity, ?

Question

CS International
CSE Physics (Chapter 5 Momentum)
Two equally weighted objects of mass m are moving in opposite directions, one with half
the velocity of the other. If they collide and stick together, what is the resultant
velocity in terms of the faster object’s velocity,

?

UpStudy AI · Accepted Answer

1. Let the masses be $$ m $$. Assume the faster object moves to the right with speed $$ v $$ and the slower object moves to the left with speed $$ \frac{v}{2} $$.

2. The momentum of the faster object is  
   $$
   p_1 = m v
   $$  
   and the momentum of the slower object is  
   $$
   p_2 = -m \left(\frac{v}{2}\right) = -\frac{mv}{2}.
   $$

3. The total momentum before the collision is  
   $$
   p_{\text{total}} = p_1 + p_2 = m v - \frac{mv}{2} = \frac{mv}{2}.
   $$

4. Since the objects stick together after the collision, their combined mass is  
   $$
   2m.
   $$

5. By conservation of momentum, the velocity $$ v_f $$ of the combined object is given by  
   $$
   2m \, v_f = \frac{mv}{2}.
   $$

6. Solving for $$ v_f $$ gives  
   $$
   v_f = \frac{\frac{mv}{2}}{2m} = \frac{v}{4}.
   $$

The resultant velocity in terms of $$ v $$ is  
$$
\boxed{\frac{v}{4}}.
$$
The resultant velocity after the collision is $$ \frac{v}{4} $$.

CS International
CSE Physics (Chapter 5 Momentum)
Two equally weighted objects of mass m are moving in opposite directions, one with half
the velocity of the other. If they collide and stick together, what is the resultant
velocity in terms of the faster object’s velocity, ?

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CS International CSE Physics (Chapter 5 Momentum) Two equally weighted objects of mass m are moving in opposite directions, one with half the velocity of the other. If they collide and stick together, what is the resultant velocity in terms of the faster object’s velocity, ?

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CS International
CSE Physics (Chapter 5 Momentum)
Two equally weighted objects of mass m are moving in opposite directions, one with half
the velocity of the other. If they collide and stick together, what is the resultant
velocity in terms of the faster object’s velocity, ?